Diffusion models for volatility have been used to price options while ARCH models predominate in descriptive studies of asset volatility. This paper compares a discrete-time approximation of a popular diffusion model with ARCH models. These volatility models have many siimilarities but the models make different assumptions about how the magnitude of price responses to information alters volatility and the amount of subsequent information. Several volatility models are estimated for daily DM/ exchange rates from 1978 to 1990.